I reiterate Webster's definition of "free market" - which you expressly agreed with:
" an economic market or system in which prices are based on competition among private businesses and not controlled by a government ", my emphasis.
You need to show that the Gov. is somehow directly controlling prices "among private businesses" - who to my knowledge do not pay GST or VAT - such as thwarting price dumping which stifles competition.
Instead, you seem to be arguing for a completely unregulated market, which however is not supported by the definition. Indeed, I could argue that the gov. is controlling the oil price by warring; or that a mosquito farting in the jungle turns into a hailstorm destroying crops controls prices; or that a company employing "slave labor" moves into an area and dumps prices controls prices - the definition is however much narrower.
Besides, even if you managed to show that it's not a free market according to the definition above, you still need to show that the money paid for GST or VAT, in turn, was not competed for and not put to good use, such as infrastructure, education, medical etc. and that a completely unregulated market would have disposed of those resources more efficiently - good luck!
Some companies , closer to politicians, can get VAT cuts on certain products.
Also the VAT is not uniform for all products, thus it will create a gap between the supply & demand.
If you have say 5% VAT on bread, and 4% VAT on restaurant menu's, then the restaurant is better off if they produce the bread themselves instead of buying it from a bakery, since they save 5% VAT on it, and only pay the 4% vat on every menu served.
This example clearly shows how the economy is distorted by them. Not to mention the wallets of the consumers.
Direct/indirect doesnt matter, the influence is pretty big, and you cant deny it, thus it is not a free market, that is heavily controlled, or at least influenced.
The dictionary definition is correct, but it is very narrow, the free market is a broader definition, while that definition is correct, thats only 1 pillar of the free market. Far more criterias need to be correct in order for us to talk about free market for example:
-Absolutely no government interference in the market: no regulation ,no taxes, no interfering laws ,and no quotas
-Free creation of marketplaces that facilitate the supply & demand exchange
-No interference in the natural exchange cycles
-Free choice of the nature,quantity, quality, price, and currency, of the tradable item/service.
Without those criterias, I would not talk about free market.